How to Factor Air Resistance into Basketball Trajectory Calculations?

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Discussion Overview

The discussion centers around incorporating air resistance into the theoretical trajectory calculations of a basketball rolling down a ramp and free falling. Participants explore various aspects of drag, measurement techniques, and the complexity of modeling the motion accurately.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant seeks advice on how to factor air resistance into their calculations for a basketball's trajectory after rolling down a ramp.
  • Another participant suggests that drag may not significantly affect the setup due to the relatively low impact velocity of 5.58 meters per second.
  • A participant emphasizes that the level of accuracy required and uncertainties in the experiment will influence the relevance of air resistance.
  • Concerns are raised about measuring speed and time of flight accurately, with one participant proposing to conduct test runs to compare theoretical predictions with actual measurements.
  • There is a mention of the complexities introduced by the spinning motion of the basketball and its horizontal velocity component affecting air flow.
  • Some participants note that standard models for air resistance include drag proportional to speed at low speeds and proportional to speed squared at high speeds.
  • One participant expresses uncertainty about how to calculate the uncertainty of tracking measurements and how to include air resistance in their theoretical model.
  • A suggestion is made to create an empirical model by comparing measured results with ideal conditions to assess the impact of air resistance.
  • Another participant provides a method to account for drag in calculations, suggesting that it may be negligible at the speeds involved.
  • One participant indicates a willingness to abandon the idea of factoring in air resistance due to a lack of calculus knowledge, while another encourages justifying the assumption of no drag.

Areas of Agreement / Disagreement

Participants express a range of views on the significance of air resistance in the experiment, with some arguing it may be negligible while others suggest it should be considered. There is no consensus on how to incorporate air resistance into the theoretical model.

Contextual Notes

Participants highlight limitations in measurement techniques and the complexity of modeling air resistance, particularly with changing velocities and the effects of spinning. The discussion remains open regarding the best approach to factor in air resistance.

gex
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Hi all, I will be doing an experiment in which I will be rolling a basketball down an elevated ramp. After leaving the ramp, the basketball will free fall for 1.25m before reaching the ground. I was looking to come up with a theoretical trajectory for the motion of the ball, the issue is that I am not sure how I would go about factoring in air resistance into my calculations. Any starting points would be much appreciated.

-Thank you in advance
 
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Drag is proportional to speed, I don't believe it will be a factor in your set up.
 
I calculated that the ball will have an impact velocity of 5.58 meters per second, so in your opinion the velocity is too low to be greatly affected by air resistance?
 
Really depends on what level of accuracy is required and the uncertainties in the whole experiment.

How you going to measure the speed or time of flight?
 
Tracking software will be used to measure speed and time of flight, but in an attempt to increase my grade I want to theoretically calculate the motion of the ball to backup my hypothesis, I know how to do this without air resistance being a factor but am struggling in finding a method to factor it into my calculations to make my theoretical model as accurate as possible. Thank you for your replies houlahound.
 
Why don't you do some test runs and see how far the measured results are a way from the theory.

What are the errors/uncertainties in your measurement tracking vid.
 
Keep in mind you have a spinning falling ball with a horizontal velicity component, very complex air flow.
 
I'm not quite sure how I would go about calculating the uncertainty of the tracking, and my issue is that i do not know how I would include air resistance in my theory. Because the velocity of the ball is constantly changing during its fall, I have no clue how I would account for the force of air resistance in my calculations.
 
There are models that account for air resistance, not simple math. I think you need to make an empirical model by seeing how far from ideal (no resistance) you are.

ETA, the standard models are;

Low speed, drag proportional to speed

High speed, drag proportional to speed squared.
 
  • #10
I see, I will probably just give up on the idea of air resistance as I'm only in high school haven't learned calculus yet. I will just stick to assuming no air resistance for my model. Thanks for your help houlahound.
 
  • #11
Well you haven't determined if you have a problem yet until you compare the basic theory with your measurement.

You will achieve more by justifying your no drag assumption.

Good luck.
 
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  • #12
gex said:
Tracking software will be used to measure speed and time of flight, but in an attempt to increase my grade I want to theoretically calculate the motion of the ball to backup my hypothesis, I know how to do this without air resistance being a factor but am struggling in finding a method to factor it into my calculations to make my theoretical model as accurate as possible. Thank you for your replies houlahound.

Drag varies as the square of speed. So if you add drag to the force balance, it will be a constant times speed squared. you have accounted for drag. But if the constant is small, it does not change the results much.

Estimate the constant by a guess that the terminal velocity is 120 mph (176 fps). At terminal velocity, drag force equals weight.
But at your speed, drag will be only 0.0017 times the weight. That is negligible, but you will have accounted for it. If someone challenges your arbitrary guess of 120 mph, repeat the calculation with 240 mph and 60 mph as the assumed terminal velocity and show that the end result does not change significantly. Drag is insignificant with all three guesses of terminal velocity.Good luck
 
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  • #13
Thank you so much for helping guys :)
 

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